Phase-comparison radiolocation system



Nov. l5, 1955 s. KAUFMAN PHASE-COMPARISON RADIOLOCATION SYSTEM Filed Oct. 16, 1950 www. A

, ZOrEFm 2,724,114 PHASE-COMPARISON RADIOLQCATION SYSTEM Sidney Kaufman, West University Piace, Tex., assign-or to Shell Deveiopment Company, Emeryviiie, Caiif., a corporation of Delaware applicati@ october 16, 195e, serial No. 190,307 s Claims. (ci. 343-105) i This invention pertains to methods and apparatus for radiogoniometric point location, andrelates more particularly to a self-modulated single-channel phase-comparison radiolocation system capable of accurately determining the location of a point, such for example as that of any instantaneous position of a Vmovable receiving station, with regard to predetermined lreference points, such as fixed transmitting stations.

Radiogoniometric location systems have an extensive applicationinnavigatiornlboth on sea and in the air, and in surveying, especially in desert and water covered areas devoid of landmarks. In this Connection, their application for purposes of olf-shore geophysical exploration may be particularly mentioned.

Radiogoniometric location systems heretofore developed and used are subject to certain limitations with regard to accuracy, range, equipment required, etc. Their main drawback may however, be said to be that ofrequiring the use of at least two channels, which considerably restricts their usefulness in view of the limited range of carrier bands made available for this purpose by government regulations.

It is therefore an object of this invention `to provide a phase-comparison radiolocation method and apparatus whereby the location of a desired point, such as that of a mobile receiving station, can be accurately determined by means of a plurality of signals transmitted thereto from a plurality of fixed stations on a single radio frequency channel.

It is also an object of this invention to provide a phasecomparison radiolocation method and apparatus whereby the location of a mobile station can be accurately determined by transmitting thereto modulated and unmodulated radio-frequency signals differing from each other by an audio frequency, obtaining audio-frequency signals by interference between and by demodulation of said radiofrequency signals, and comparing the phases of selected harmonics of said audio frequency signals.

These and other objects of this invention will be understood from the following description taken with referenc to the attached drawings wherein:

Fig. l is a schematic diagram of the present system;

Fig. 2 is an equivalent arrangement of a portion of the mobile station shown in Fig. 1. t

Referring to Fig. l, the-present single-channel phasecomparison radiolocation system comprises three xed reference stations generally indicated as 1, 2 and 3, and any desired number of mobile stations at points whose location it is to determine with regard to the reference points. For purposes of simplicity, only one of these stations is shown at 4 in Fig. l.

The reference stations 1, 2 and 3 are preferably located along an approximately straight line, and are separated from each other by-distances which may be as large as desired and are limited' only by the power and the sensitivity of the transmitters and receivers used.

The central reference stat'on comprises Va transmitter 20 provided with an antenna 21. Y

lrates Patent] a desired carrier radiofrequency f2.

2,724,114 Patented Nov. 15,1955

The lateral reference station 1 has a transmitter 10 provided with a transmitting antenna 11. Station 1 has also a receiver 13 provided with an antenna 12 and connected in circuit with a filter section or unit 14, a frequency multiplier 15 and a modulator 16, whose output is applied to modulate the transmitter 10. The two antennas may be separated by a distance such as 50 feet.

Similarly, the other lateral station 3 has a receivingantenna 32, receiver 33, filter 34, frequency multiplier 35, modulator 36and a transmitter 30 with antenna 31.

The mobilel station 4, which may be, for example, a vehicle, a plane ora ship, such as a ship doing geophysical exploration work, hasra receiving antenna 42 and a receiver 43, whose detector section is of the so-called square law type, which does not detect linearly, but squares 'the input, Receivers 13 and 33 of stations 1 and 3 are also preferably of this type. The receiver 43 is diagrammatically shown as comprising a radio-frequency amplifier section 44 and a detector section 45.

The audio-frequency output of the receiver 43 is connected to audio-lilters 46, 47, 56 and 57, frequency multipliers V48 and 58, and phase meters 49 and 59.

The central reference station 2 is adapted to vtransmit Although even relatively low radio frequencies may be used with the present system vto increase operational range while retaining 'the desired high accuracy, the invention will be described with reference to the use of high frequencies of the order from l to 5 megacycles, which are technically highly satisfactory for achieving the desired results and whose use maybe Y found permissible under existing government regulations.

v The transmitter 10 of station 1 is adapted to transmit a basic carrier frequency f1, which differs from the frequency f2 only by an audio frequency w1 of low order,

o such for example as 400 cycles, so that f1=f2lw1.

In a similar manner, the transmitter 30 of station 3 is adapted to transmit a basic carrier frequency f3, which diers fromlthe frequency f2 by another low audio frequency w3, :such for example as 250 cycles, so that fs=fl2,-wa. l

The low order audio frequencies w1 and w3 should preferablybe chosen s o as not to be harmonically related to each other in a simple ratio, for example, frequencies Vsuch as 250 and 400 cycles, 350 and 600 cycles, etc., may

be advantageously used.

Each of the receivers 13, 33 and 43 of the Vsystem is tuned to the carrier frequency f2, and all three receivers are therefore responsive to all three transmitters 10,7120 and 30, since the three frequencies f2, f1=fz+w1 and f3=f2-w3, for example 1,800,000 cycles, 1,800,400 cycles and 1,799,750 cycles, are too close to each other to be separated from each other by the radio-frequency sections of the receivers 13, 33 and 43.

At stationl, the lter unit 14 is designed to pass only the beat or interference frequency between the frequency fzrreceived from transmitter 20 of station 2 and the frequency f1 from transmitter 10 of station 1, that is, the audio frequency w1=f1*f2. This audio frequency is supplied to the frequency multiplier unit 15, which multiplies, that is, doubles, triples, etc., said frequency, thus converting it toa frequency which may be designated vas nwi, where n is any preferable low integer.V The audio frequency nwi is then fed to the modulator unit 16, which Y applies it to modulate the basic carrier frequency fr of transmitter 10. The transmitter 10 thus transmits a complex signal, which may for convenience be consideredfas comprising the basic radio frequency component f1 and aV the l'ter unit 34 passes a beat frequency w3=f2-f3, and the transmitter 30 transmits a complex signal F, having a component f3, and a modulated component f3 (mod.) nws.

When the whole system is in operation, the following signals are thus being transmitted by its three transmitting stations, only one channel, that of the carrier frequency f2, being require for this purpose:

Station 1 transmits signals f1=f2lw1 and F1=f1 (mod.)

il'wi.

Station '2 transmits signal fz.

Station 3 transmits signals f3=f2w3 and F3=s (mod.) n'w3.

The radio-frequency amplifier 44 of the receiver 43 of the mobile indicator station 4 is responsive to all these signals, and the output of the detector section 45 .is a complex audio signal consisting of a group of signals or components of dilferent audio frequencies.

The Vfilter 47 is preferably designed to select only the component (mod.) nwl due to demodulation of F1 in 45, which is passed to the phase meter 49.

The filter 46 is preferably designed to select only the component w1 due to interference between the radio-'frequency signals f1 from station 1 and f2 from station 2. This signal of frequency w1 is passed `to frequency multiplier 48, which, for vthe abovementioned characteristics of filters 47v and 46, multiplies the frequency of w1 by the factor n. The signal of frequency nwi thus obtained is supplied to the phase meter 49, which compares its phase with Vthat of the signal of frequency (mod.) nw1, suppiiedvto said meter through filter 47, as previously described.

In the same manner the meter 59 may compare the phase of vthe modulating audio frequency (mod.) nwa supplied thereto from filter y57, with that of the audio fre-Y quency nw supplied thereto as a result of selection -by filters of the signal of frequency w3 arising lfrom interference between the radio-frequency signals fz 'from station 2 and ja from station 3, and after frequency multiplication -in frequency multiplier 58. Y

With regard to the two audio-frequencies compared by the phase-meter 49, it will be seen from the discussion hereinbelow that the frequency (mod.) nw1, obtained by demodulation, is essentially not phase-related to the position of the mobile station 4 with regard to the location of stations 1 and 2, whilethe other frequency, namely nwi, obtained from interference Ybetween f1 and fz and subsequentfrequency multiplication, is phase-dependent on the position of the mobile unit 4 with regard .to .the location of stations 1 and 2.

In other` words, the instantaneous phase of .the interference or beat note between the signal f2 from station v2 and the signal f1=fzlw1 from station 1 is a function of the difference lin path lengths between the mobile station '4 and the two transmitting stations 1 and 2. When the beat note is multiplied, .for example, doubled, tripled, etc. in frequency vby the unit 4S, the 'change 'in phase of the multiplied, i. e. doubled, tripled, etc. .beat note becomes a multiple, i. e. two times, three times, etc. of the basic beat note. If Vthe mobile station yis -moved or displaced in a manner such that the difference in distance between said :mobile station 4 and the fixed transmitting stations v1 and 2 changes, .then the phase of the multiplied beat -note willchange. y

On 'the otherhand, the ,phase of the (mod.) nwi Aaudio frequency -signal due to the demtdulation of the modulatedradio-frequency signal fFi=f1 '(mod.) nw1 from stationv lfis essentially constant in space, event for large changes 'in the location of the mobile station 4. This signal. can therefore be used as .a reference .signal to measure the .phase changes of the multiplied beat signal caused by changes .in location lof the .mobilestatiom which is -done by comparing the phase o'f the nw1 land (mod.) nwi audio frequency signals in fthe phase meter '49.

lt may be shown that in cases wherein the phase indication at a .mobile station :depends 'on the difference "in distance between said mobile station and twoxed stations, there exist lhyperbolic lines Vof position along which the phase indication is constant. Knowing the line of position through a starting point, and continuously measuring and counting cycles and fraction of a cycle of the multipled beat note while moving from the starting point to a final point, it is possible to determine the hyperbolic line of position of the final point. In order to determine uniquely the position of the final point on the hyperbolic line, however, it is necessary'to determine the point 'of intersection of said line with a second hyperbolic line of position, which is accomplished in the present system by means of the two other audiofrequency signals whose phases are compared by the second phase meter 59 in a manner identical to that already described with regard to meter 49 to give a second hyperbolic line of position for the location of the mobile station 4. This second line of position passing through the location of the mobile station is one of a `family of hyperbolas having the locations of stations 2 and 3 as foci, in .the same manner as the family of hyperbolas obtained by phase comparison in meter 49 has 'stations 1 and 2 as foci. The simultaneous measurements effected by meters 49 and 59 are` thus su'fticient for a positive and accurate determination of the location of the mobile station 4 at any given moment.

For clearness, .the above may be .recapitula'ted with regard to an example in which numerical values are assigned to the various frequencies of the system:

Carrier frequency assigned to system: jz=l.8 .megacycles= 1,800,000 cycles/ sec.

Fixed station I 4. VComplex modulated signal from 'station 1: F1=f1v (mod.) -nw1=1,800,400 cycles (radio frequency of 1,800,400 C. P. S. modulated by an audio frequency of 800 lC. P. S.').

Fixed Station 2 ,Basicn'equency f2=.1,'soo,ooo C. P. s.

Fixed Station 3 l. Basic frequency: fs=f2-w3=l,799,750 C. P. S.

2. Frequency obtained by interference of stations 2 and 3: f2'-`f3=w3=250 C. P. S.

Y 3. Modulating frequency after .frequency multiplicar tion: nw3=500 C. P. S.

4. Complex modulated signal from .station 3: Fa=j3 (mod.) nw3='1,799,750 C. P. S. (radio frequency of 1,799,750 C. P. LS'. modulated .by `an audio .frequencyrof 500 C. P. 8.).

Mobile station 4 y 1. Audio-.frequency .signal obtained by interference between the frequency ffz from `station 2 and frequency 'f1 from station 1: w1=400 C. -P. S. (shifting phase).

v2. After .frequency multiplication: nw1=800 cycles (shifting phase).

3. Frequency obtained by demodulation of the complex .modulated signal F1: (mod.) kiwi-:800 C. l. S. (constant phase) 4. .Frequencies compared by meter 49: 800 fC.-P. 5S. (shifting phase) and 800 C. P.S. (constant phase).

.5. Audio-frequency signal obtained byinterference between frequency fz from station 2 and frequency f3 from station 3: w3=250 C. P. S. (shifting phase).

6. .After frequency multiplication: nw3='500 C. P. S. (shifting phase).

7. Frequency obtained by .demo'dulation vof fthe "corn-v pl'ex 'modulated signal F3: (mod.) mus-:500 C. P. S. (constant phase).

1S. Frequencies compared l'by meter l59: 500 C. "P. S. (shifting phase) and 500 C. S. (constant phase).

VAs will appear hereinbelow, there are other lchoices among the components of the complex audio signal from 4S, besides those selected for the numerical example above, which may be advantageously used for the phase comparison process. In certain of these cases the signals from lters 47 and 57 may be passed to frequency multipliers 48a and 58a respectively, thence to meters 49 and 59 respectively. In these cases the multiplication factors of 48a and 58a are not the same as those of 48 and 58 respectively. Nor will the multiplication factors of 48 and 58 be necessarily the same as those of 15 and 35 respectively. In any event the components of the complex audio signal must be so selected, and the frequency multipliers Vso arranged, that the frequenciesof the two signals being supplied to meter 49 are alike and that the phase angle indicated by meter 49 is a function of the difference n path lengths between the mobile station 4 and the two fixed stations 1 and 2; also that the frequencies of the two signals being supplied tol meter 59 are alike and that the phase angle indicatedy by meter 59 is a function of the difference in path lengths between the mobile station 4 and the two fixed stations 2 and 3.

In discussing the theory of operation of the present system, it is generally sutcient to consider that portion thereof comprising the central transmitting station 2, one of the lateral transmitting stations, for example, station 1, and one portion of the mobile indicator station 4, for

example,'that portion comprising the phase meter 49. Asl

stated hereinabove, this portion is sufficient for determining a hyperbolic line of position passing through the pointV of observation, that is, station 4. Furthermore, since the audio frequencies w1 and w3 are not related in simple harmonic fashion, the operation of this portion of the system will be substantially unaffected by the functioning of the remaining portion of the complete system.

. Considering first the case of heterodyne action between two unmodulated transmitters, it Amay be shown that the alternating current output of a receiver whose detector' is a non-linear one of the square-law type, after radiofrequency filtering, will be proportional to:

2E1E2 cos [21rw1t-(A1-Az)] (l) wherein:

E1 and E2 are the carrier frequency voltages of stations 1 and 2 respectively, t is time,

and

wherein: v

r M is the degree of modulaton'having a value between O'and 1, g`=A32(A.1-A2),

bisf the initial phasing-of the modulating-signal,y '.z-'- g1".

If the receiver output given by Equation (2) vis passed through a lter tuned to w1, the filter output is proportional to.

If the distance between antenna 12 and antenna 11 is equal to su, and the distance between antenna 12 and and antenna 21 is equal to s2, then the signal expressed by Equation (2) is available from receiver 13. Then if ii1ter'14 is tuned to frequency w1, its output is given by Equation (3). In order to obtain self-modulation at station 1, the signal expressed by Equation (3) is multiplied or doubled in frequency by the multiplier or doubler 15 and applied by the modulator 16 to the transmitter 10.

Under these conditions of self-modulation it can be shown that the phase angle of the signal expressed by Equation (3.) is related to the phase angle of the modulating signal in such a manner that h :tan-1 The amplitude of the component of frequency wrof the detected signal at the mobile station 4 will therefore depend on the value of (s4-ssh If (sv-ss): changes, the amplitude will change periodically between. the limits E1E2(2|M) and EiE2(2-M) over intervals s4-S3=L2/2, where L2 is the wave length of thefrequency f2 transmitted from station 2. The circuits to which this signal is applied must therefore be designed; with such constants that their operation is unaffected by the breathing or periodic variation of the signal level.

It may also be shown from the equations given hereinabove that the readings of phase meter 49 are not -af-y fected by changes in phasing between transmitting stations 1 and 2 nor by changesin the carrier frequency of station 1,.the same being true of the phase meter 59 with regard to the phasing of stations 2 and 3 and'th'e carrier frequency of station 3.

O'n the other hand, the readings of the phase meter `49 (and also of-y phase meter 59).are affected by' changes of the carrier frequency f2 of station 2, although this effect is very small, as may be seen from the following.

It may beshown that this effect is at a maximum when IIL-:Bind 41rf M2+4+4M cos'lK-lc2 (S4-"Sail wherein y is the -phase meter reading, and A,Kairi-2p.

Equation 8 holds for all values of M between 0 and 1. For the particular case M :0, the phase meter reading is which indicates `a linear relationship between y1 and the value Yof (sir-t-sa). The loci of positions of constant phase readings will therefore lie on one of a family of hyperholas whose foci .are .at stations 1 and 2.

For other values of M, therevare slight deviations from thisiinearity. if `a hyperbolic grid 'system is used, the phase meter reading will the in error by an amount depending on the modulation factor, the position within the lane, and the wave length L2. Considering, for simplicity, a case of motion of the mobile station along the base line, it may be shown that, for M =1, the peak error will be L2/24 and for M :0.5 it will be approximately L2/48. At a point away from the base line, the error will increase due to lane expansion.

It is not practical to apply a correction to the phase meter reading to eliminate this error, since this would require the phase meter to record absolute phase differences at eachpoint, rather than relative lphase changes inmoving from a point to another. -This error may lhow ever 'be rendered negligible by a proper selection of M, Lz, and other operating factors.

- The `method so far described involved, rst, self-modulation yat twice the beat frequency between the -ca-rr'ier frequencies f1 and f2 from stations 1 and 2, and, second, phase comparison between the doubled w1 component obtained by interference and the (mod.) 2w1 component obtained by demodulation. It has been seen that some error ,arose because the angles G of `Equation V(6), and the :angle I-I, leorresponding, for spacings .sa and s4, to the angle 1h of VEquation (3), are 'both non-linear functions of-(ss-sa.

it may therefore be preferred to apply the method of the present invention by modulating at twice the beat frequency and using a frequency tripler for phase vcomparison between :the second and third harmonics of the complex signal.

It will be seen that the sixth term of Equation (2) foon taining the 31a-lue 61u, relates to the thirdvoltage harmonic of Dthe :interference signal Areceived at station 4. 'If this voltage is filtered and passed through a frequency doubler, the output Ywill be proportional to:

wherein values A11, A21 and A31 correspond, for spacings be a reference (constant phase) voltage proportional 1o 2E12M -cos .(,l21rw1-t-3A3U (ll) I Phase comparison between the two signals will therefore result in a phase reading the .maximum possiblev Aerror is 1.2 degrees as comparedv withIP-:L degrees mentioned hereinabove.

8 A hyperbolic system of even greater inherent precision can be obtained if -a different pair of components of the composite signal is used for phase comparison.` v Thus, referring again to Equation (2) and quadrupling the frequency of the 61rw1 component, there Yis obtained a signal proportional to Y `Y ElEzMeos r241rwn-4A31-4m11-A21N ('13) lIf `.the frequency of the 81rw1 component is tripled, a signal is obtained which is proportional to It will be seen that the phase reading :ya changes here by 21r over intervals of (s4--S3).=L2/4, S0 that lthe in herent precision is twice that of the systems which :indir cate the values of y1 or ya.

Those components ofthe composite signal whose amplitudes depend on the product of the two transmitter fields .are more desirable for use than the components whose amplitude depends only on the eld of one transmitter, since the former are more uniform over `the area of operation, When the trequency multiplication n has a value of 2, fit may be .seen from Equation (2) that only theVZ-'rwl'and 61rw1 .components havearnplitude dependF ence on B1B@ but Ythat the former has amplitude breathing and phase distortion, whereby its Vuse involves some draw backs. To obtain the advantage yof a more uniform signal without breathing or distortion, it is possible to use the present system with modulation at three, four or more times the beat frequency, that is with vfrequency multipli.-

cation wherein 11:3 or 11:4, etc. Although this calls for a some-What broader ltransmission bandwidth, the only modification required of the apparatus Vused is .a ,suitable change of filters. Y

lf, for example, a frequency multiplication and modulation is used such that 11:3, Equation (2) becomes:

2 Y E2M2 +2E1E2 Cos [21rw.z-(A,-A,)]+

ponent, it may be shown that the phase meter reading will be z: ya c Thus, the phase reading y, varies in such cases periodi- :ally over intervals (s,-s) f..t-L,/3, VThe :same in percent.

however, both signal amplitudes are proportional to ErEaM. K

It is obvious from the preceding that other pairs of components can be used for .phasecomparison pur-poses and that the inherent accuracy ofthe vsystem .is increased by using higher values of n. It should be kept in mind howerver vthat the yanalysis ,presented hereinabove dealt only with one half of the system, that invloving transmitting `stations 1 and 2, since the other half, that involving stations 2 and 3, functions in exactly the same manner to give the second desired Vfamily of hyperbolas. However, even when the audio frequencies w1 and `u3 areselectcdb as not to be harmonically related to each other in simple fashion (such as 4Q() and 250 cycles) the modulation and the intermodulation components, and their harmonics, of

9 both halves of the system must be considered. With increased value of n and higher frequency multiplication, the required separation of components introduces practical difculties which limits the maximum value of n.

I claim as my invention:

1. ln a method of phase-comparison radiolocation, the steps of transmitting three signals on a single radio frequency channel from three fixed stations, the radio frequency of each of said signals differing from the others by a predetermined audio frequency, receiving said signals at the first station and obtaining a first audio frequency at said station by interference between the signals from the rst and second stations, applying solely said audio frequency to modulate the signal transmitted by the first station, receiving said signals at the third station and obtaining a second audio frequency at said station by interference between the signals from the second and third stations, applying solely said second audio frequency to modulate the signal transmitted by the third station, receiving the signals from the fixed stations at a mobile station, obtaining a first audio frequency signal by interference between the signals from the first and second stations, obtaining a second audio frequency signal by demodulating the signal from the rst station, obtaining a third audio frequency signal by interference between the signals from the second and third stations, obtaining a fourth audio frequency signal by demodulating the signal from the third station, simultaneously comparing the phases of said first and second and the phases of said third and fourth audio frequency signals, and determining the position of the mobile station from said simultaneous phase comparison.

2. ln a method of phase-comparison radiolocation, the steps of transmitting three signals on a single radio frequency channel from a central fixed station and two lateral fixed stations each located to one side of said fixed station, each of said signals being transmitted by one of said stations, the radio frequency of each of said signals differing from the others by a predetermined audio frequency, receiving the signals from the central station and one of the lateral stations at said lateral station and obtaining a lirst audio frequency at said station by interference between said two signals, multiplying said audio frequency, applying solely said multiplied audio frequency to modu late the signal transmitted by said first lateral station, receiving the signals from the central station and the second lateral station at said second lateral station and obtaining a second audio frequency by interference between said last two signals, multiplying said second audio frequency, applying solely said multiplied second audio frequency to modulate the signal transmitted by the second lateral station, receiving the signals from the three fixed stations at a mobile station, obtaining a rst audio frequency signal by interference between the signals from the first lateral and the central stations, multiplying said frequency by a factor equal to that used at the first lateral station, obtaining a second audio frequency signal by demodulating the signal from the iirst lateral station, ob-

taining a third audio frequency signal by interference between the signals from the central and the second lateral stations, multiplying said frequency by a factor equal to that used at the second lateral station, obtaining a fourth audio frequency signal by demodulating the signal from the second lateral station, simultaneously comparing the phases of said first and second and the phases of said third and fourth audio frequency signals, and determining the position of the mobile station from said simultaneous phase comparisons.

3. in a method of phase comparison radio-location, the steps of transmitting signals on a single radio frequency channel from a first and a second station, said signals differing from each other by an audio frequency, receiving said signals at the irst station and obtaining said audio frequency by interference between said two radio frequency signals, multiplying said frequency by a factor having the value of a small integer, applying solely said multiplied audio frequency to modulate the signal transmitted by the first station, receiving said signals at a mobile station, obtaining a first audio frequency signal by interference between said radio frequency signals, selecting a harmonic of said audio frequency signal, obtaining a second audio frequency signal by demodulating the radio frequency signal from the rst station, selecting a harmonic of said second audio frequency signal, said second selected harmonic being of an order different from that ot` the first selected harmonic, multiplying one of said harmonics so as to make its frequency equal to that of the other harmonic, and comparing the phases of said two harmonics.

4. in a method of phase comparison radio-location, the steps of transmitting signals on a single radio frequency channel from a iirst and a second station, said signals diering from each other by an audio frequency, receiving said radio frequency signals at the rst station and obtaining said audio frequency by interference between said two radio frequency signals, multiplying said frequency by a factor having the value of a small integer, applying solely said multiplied audio frequency to modulate the signal transmitted by the first station, receiving said radio-frequency signals at a mobile station, obtaining a first audio frequency signal by interference between said radio-frequency signals, selecting a harmonic of said audio frequency signal, said harmonic being of an order M having the value of a small integer, multiplying said harmonic 'by a factor N having the value of a small integer, obtaining a second audio frequency signal by demodulating the radio frequency signal from the first station, selecting a harmonic of said second audio frequency signal, said second selected harmonic being of the order of M1, having the value of a small integer, multiplying said harmonic by a factor N1 having the value of a small integer, said factors and said orders of harmonics being so chosen that NM =N1M 1, and comparing the phases of the two selected multiplied harmonies.

5. The method of claim 4 wherein the values of M, N, M1 and N1 are small integers having a value not less than 1 and not more than four.

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